Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

In problems 3-6, use the figure to solve each inequality. 

a) $g\left(x\right)\ge f\left(x\right)$

b) $f\left(x\right)>g\left(x\right)$

Step-by-Step Solution

Answer

(a) $[-2,1]$

(b) $(-\infty ,-2) or (1,\infty )$

Part (a) Step 1. Given Information

It is given that $g\left(x\right)\ge f\left(x\right)$ and the graph is,

Part (a) Step 2. Observe the graph

• From the graph, it is observed that the value of $g\left(x\right)$ is greater than or equal to $f\left(x\right)$ for $-2\le x\le 1$.
• In the set builder form, for $g\left(x\right)\ge f\left(x\right)$, $\left\{x\right|-2\le x\le 1\}$. Also, in interval notation it is denoted as $[-2,1]$.

Part (b) Step 1. Given Information

It is given that, $f\left(x\right)>g\left(x\right)$ and the graph is,

Part (b) Step 2. Observe the graph

• From the graph, it is observed that the value of $f\left(x\right)$ is greater than $g\left(x\right)$ for $x<-2 or x>1$.
• In the set builder form, for $f\left(x\right)>g\left(x\right)$, $\left\{x\right|x<-2 or x>1\}$. Also, in interval notation it is denoted as $(-\infty ,-2) or (1,\infty )$.